Cartans in Clifford-G3C.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cartan's Rotation Algorithms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "from clifford import eps\n",
    "from clifford.tools import orthoFrames2Verser\n",
    "from clifford.tools.g3c import * \n",
    "from scipy import e,rand"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "works\n"
     ]
    }
   ],
   "source": [
    "subspace = e123 # can change to e12 to test g2 operations\n",
    "\n",
    "def generate_rotation_rotor():\n",
    "    B = subspace.project(random_bivector())\n",
    "    return e**B\n",
    "\n",
    "def generate_translation_rotor():\n",
    "    a = subspace.project(layout.randomV())\n",
    "    return (1 + ninf *a / 2)\n",
    "\n",
    "# generates random vectors in g3\n",
    "euc_vector = lambda: subspace.project(layout.randomV())\n",
    "\n",
    "# Create random euclidean transformation from translations  and rotation\n",
    "T = generate_translation_rotor()\n",
    "R = generate_rotation_rotor()\n",
    "D = generate_dilation_rotor(rand())\n",
    "V = T*R*D\n",
    "\n",
    "\n",
    "a = [euc_vector() for k in range(4)] # create set of 4 vectors\n",
    "A = list(map(up,a)) #\n",
    "# homo() ==down/up roundtrip. observations are in g3, not g3c, so \n",
    "# this is represented by doing a down/up round trip, which is just homo()\n",
    "B = [homo(V*k*~V) for k in A] \n",
    "\n",
    "V_found,rs = orthoFrames2Verser(A=A,B=B, remove_scaling=True,det=1)\n",
    "\n",
    "if (min( abs(V_found+V),abs(V_found-V)) <eps() ):\n",
    "    print('works')\n",
    "else:\n",
    "    print('fails')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.99714 - (0.02005^e12) + (0.09564^e13) - (0.24437^e14) - (0.24437^e15) - (0.03431^e23) + (0.55138^e24) + (0.55138^e25) - (0.67557^e34) - (0.67557^e35) - (0.0704^e45) + (0.03089^e1234) + (0.03089^e1235) - (0.00142^e1245) + (0.00675^e1345) - (0.00242^e2345),\n",
       " 0.99714 + (0.02005^e12) - (0.09564^e13) + (0.24437^e14) + (0.24437^e15) + (0.03431^e23) - (0.55138^e24) - (0.55138^e25) + (0.67557^e34) + (0.67557^e35) + (0.0704^e45) - (0.03089^e1234) - (0.03089^e1235) + (0.00142^e1245) - (0.00675^e1345) + (0.00242^e2345))"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "V_found,V"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 loops, best of 3: 5.31 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "orthoFrames2Verser(A=A,B=B, remove_scaling=True,det=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [default]",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  },
  "toc": {
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": "block",
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}